Hausdorff dimension of weighted singular vectors in R2

Lingmin Liao; Ronggang Shi; Omri N. Solan; Nattalie Tamam

doi:10.4171/JEMS/934

Hausdorff dimension of weighted singular vectors in R²

Lingmin Liao, Ronggang Shi, Omri N. Solan, Nattalie Tamam

Department of Theoretical Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let w = (w₁, w₂) be a pair of positive real numbers with w₁ + w₂ = 1 and w₁ ≥ w₂. We show that the set of w-weighted singular vectors in R² has Hausdorff dimension 2− ₁₊ ¹ _w ₁.

Original language	English
Pages (from-to)	833-875
Number of pages	43
Journal	Journal of the European Mathematical Society
Volume	22
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/934
State	Published - 2020

Keywords

Diophantine approximation
Hausdorff dimension
Homogeneous dynamics
Weighted singular vector

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title = "Hausdorff dimension of weighted singular vectors in R2 ",

abstract = "Let w = (w1, w2) be a pair of positive real numbers with w1 + w2 = 1 and w1 ≥ w2. We show that the set of w-weighted singular vectors in R2 has Hausdorff dimension 2− 1+ 1 w 1.",

keywords = "Diophantine approximation, Hausdorff dimension, Homogeneous dynamics, Weighted singular vector",

author = "Lingmin Liao and Ronggang Shi and Solan, {Omri N.} and Nattalie Tamam",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2020",

year = "2020",

doi = "10.4171/JEMS/934",

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AU - Shi, Ronggang

AU - Solan, Omri N.

AU - Tamam, Nattalie

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PY - 2020

Y1 - 2020

N2 - Let w = (w1, w2) be a pair of positive real numbers with w1 + w2 = 1 and w1 ≥ w2. We show that the set of w-weighted singular vectors in R2 has Hausdorff dimension 2− 1+ 1 w 1.

AB - Let w = (w1, w2) be a pair of positive real numbers with w1 + w2 = 1 and w1 ≥ w2. We show that the set of w-weighted singular vectors in R2 has Hausdorff dimension 2− 1+ 1 w 1.

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KW - Hausdorff dimension

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Hausdorff dimension of weighted singular vectors in R²

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